A note on SAT algorithms and proof complexity

作者：Krajicek Jan^*

来源：Information Processing Letters, 2012, 112(12): 490-493.

DOI：10.1016/j.ipl.2012.03.009

• Computational complexity

We apply classical proof complexity ideas to transfer lengths-of-proofs lower bounds for a propositional proof system P into examples of hard unsatisfiable formulas for a class Alg(P) of SAT algorithms determined by P. The class Alg(P) contains those algorithms M for which P proves in polynomial size tautologies expressing the soundness of M. For example, the class Alg(F-d) determined by a depth d Frege system contains the commonly considered enhancements of DPLL (even for small d). Exponential lower bounds are known for all F-d. Such results can be interpreted as a form of consistency of P not equal NP. Further we show how the soundness statements can be used to find hard satisfiable instances, if they exist.

• 出版日期2012-6-30